**5. Results and Discussion**

The obtained results from the above-mentioned method (HAM) are presented in the form of tables and graphs. Tables 1 and 2 display the effects of the slip on the dynamic properties of a slider, showing that normalized lift and drag decrease as the slip and/or Reynolds number increases. The lift (per area) of the strip slider was much greater than the circular slider, although the drag remained the same in both cases. The effect of slip could be substantial, affecting the drag much more than the lift.


**Table 1.** Properties of the long porous slider. Normalized lift Λ, normalized *x*1− direction drag, and normalized *x*2− direction drag.


**Table 2.** Properties of the circular porous slider. Normalized lift Λ, normalized drag −<sup>ψ</sup>/1(1).

Velocity distributions for the long and circular slider are presented graphically in Figures 7–9.

**Figure 7.** Similarity function ψ/3for the long slider.

**Figure 8.** Similarity function ψ2 for the long slider.

**Figure 9.** Similarity function ψ1 for the long slider.

For the long slider, the effect of the Reynolds number in the presence of slip and the magnetic field is shown in Figures 10–18. It is observed that the velocity profile was very much changed. It was seen that slip near the ground reduced the lateral velocity much more than slip on the slider. Moreover, increasing the magnetic parameter decreased the lateral velocity components further (see Figure 12). The effects of the Reynolds number on the typical velocity distribution for the circular slider were similar, as displayed in Figures 19–28. The behavior of velocity profiles was similar for the long and circular sliders in cases of no-slip (see Figures 19 and 20). Further, velocity profiles behaved in a similar fashion in both cases (i.e., parabolic or linear for a low Reynolds number, while a boundary layer formed near the surface in cases of a large Reynolds number). Figures 21–28 demonstrate the effect of the slip parameter on the velocity components corresponding to different Reynolds numbers. These pictorial descriptions demonstrate that velocity profiles decrease with an increase in slip parameters, and that this decrease become even greater after applying the magnetic field. This is due to the fact that slip hinders fluid particles and displaces motion in the vicinity.

**Figure 10.** Similarity function ψ/3for the long slider.

**Figure 11.** Similarity function ψ2 for the long slider.

**Figure 12.** Similarity function ψ1 for the long slider.

**Figure 13.** Similarity function ψ/3for the long slider.

**Figure 14.** Similarity function ψ2 for the long slider.

**Figure 15.** Similarity function ψ1 for the long slider.

**Figure 16.** Similarity function ψ/3for the long slider.

**Figure 17.** Similarity function ψ1 for the long slider.

**Figure 18.** Similarity function ψ/3for the long slider.

**Figure 19.** Similarity function ψ/3for the circular slider.

**Figure 20.** Similarity function ψ1 for the circular slider.

**Figure 21.** Similarity function ψ/3for the circular slider.

**Figure 22.** Similarity function ψ1 for the circular slider.

**Figure 23.** Similarity function ψ/3for the circular slider.

**Figure 24.** Similarity function ψ1 for the circular slider.

**Figure 25.** Similarity function ψ/3for the circular slider.

**Figure 26.** Similarity function ψ1 for the circular slider.

**Figure 27.** Similarity function ψ/3for the circular slider.

**Figure 28.** Similarity function ψ1 for the circular slider.

These results qualitatively confirm the expectation that a drag-like Lorentz force is created by the magnetic field normal to the lateral flow direction, and this force decreases the lateral velocity components. Lift and drag components are important physical quantities for a porous slider. It is interesting to note that the lift is free of translation, but the drag components depend on a cross flow. The effectiveness of a porous slider can be enhanced by making the ratio of friction force to lift smaller. As pointed out by Wang [16], the porous slider should be operated at a cross-flow Reynolds number below unity for optimum efficiency. According to Table 1, porous sliders should be operated at small values that are still valid even when an external uniform magnetic field is applied. Moreover, from the point of view of optimum efficiency, it is more efficient to move a flat slider on a fluid subject than in a high-intensity magnetic field.
